Answer:
0.075 ohm
Explanation:
[tex]i_{o}[/tex] = maximum value of the current
[tex]i[/tex] = value of the current after time "t = 0.35 s" = 0.65 [tex]i_{o}[/tex]
[tex]R[/tex] = resistance of the resistor = ?
[tex]L[/tex] = Inductance of the inductor = 25 mH = 0.025 H
[tex]T[/tex] = Time constant of the circuit
Current at any time is given as
[tex]i = i_{o}(1 - e^{\frac{-t}{T}})[/tex]
[tex](0.65) i_{o} = i_{o}(1 - e^{\frac{-0.35}{T}})[/tex]
[tex](0.65) = (1 - e^{\frac{-0.35}{T}})[/tex]
[tex]T = 0.333[/tex] sec
Time constant is given as
[tex]T = \frac{L}{R}[/tex]
[tex]0.333 = \frac{0.025}{R}[/tex]
[tex]R = 0.075 [/tex] ohm
